# ---
# title: 1510. Stone Game IV
# id: problem1510
# author: Tian Jun
# date: 2020-10-31
# difficulty: Hard
# categories: Dynamic Programming
# link: <https://leetcode.com/problems/stone-game-iv/description/>
# hidden: true
# ---
# 
# Alice and Bob take turns playing a game, with Alice starting first.
# 
# Initially, there are `n` stones in a pile.  On each player's turn, that player
# makes a  _move_  consisting of removing **any** non-zero **square number** of
# stones in the pile.
# 
# Also, if a player cannot make a move, he/she loses the game.
# 
# Given a positive integer `n`. Return `True` if and only if Alice wins the game
# otherwise return `False`, assuming both players play optimally.
# 
# 
# 
# **Example 1:**
# 
#     
#     
#     Input: n = 1
#     Output: true
#     Explanation: Alice can remove 1 stone winning the game because Bob doesn't have any moves.
# 
# **Example 2:**
# 
#     
#     
#     Input: n = 2
#     Output: false
#     Explanation: Alice can only remove 1 stone, after that Bob removes the last one winning the game (2 -> 1 -> 0).
# 
# **Example 3:**
# 
#     
#     
#     Input: n = 4
#     Output: true
#     Explanation: n is already a perfect square, Alice can win with one move, removing 4 stones (4 -> 0).
#     
# 
# **Example 4:**
# 
#     
#     
#     Input: n = 7
#     Output: false
#     Explanation: Alice can't win the game if Bob plays optimally.
#     If Alice starts removing 4 stones, Bob will remove 1 stone then Alice should remove only 1 stone and finally Bob removes the last one (7 -> 3 -> 2 -> 1 -> 0). 
#     If Alice starts removing 1 stone, Bob will remove 4 stones then Alice only can remove 1 stone and finally Bob removes the last one (7 -> 6 -> 2 -> 1 -> 0).
# 
# **Example 5:**
# 
#     
#     
#     Input: n = 17
#     Output: false
#     Explanation: Alice can't win the game if Bob plays optimally.
#     
# 
# 
# 
# **Constraints:**
# 
#   * `1 <= n <= 10^5`
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
